On rate-dependent polycrystal deformation: the temperature sensitivity of cold dwell fatigue

A temperature and rate-dependent crystal plasticity framework has been used to examine the temperature sensitivity of stress relaxation, creep and load shedding in model Ti-6Al polycrystal behaviour under dwell fatigue conditions. A temperature close to 120°C is found to lead to the strongest stress redistribution and load shedding, resulting from the coupling between crystallographic slip rate and slip system dislocation hardening. For temperatures in excess of about 230°C, grain-level load shedding from soft to hard grains diminishes because of the more rapid stress relaxation, leading ultimately to the diminution of the load shedding and hence, it is argued, the elimination of the dwell debit. Under conditions of cyclic stress dwell, at temperatures between 20°C and 230°C for which load shedding occurs, the rate-dependent accumulation of local slip by ratcheting is shown to lead to the progressive cycle-by-cycle redistribution of stress from soft to hard grains. This phenomenon is termed cyclic load shedding since it also depends on the material's creep response, but develops over and above the well-known dwell load shedding, thus providing an additional rationale for the incubation of facet nucleation

Microstructural heterogeneity in rate-dependent plasticity of multiphase titanium alloys

Polycrystalline rate-dependent plasticity is found to originate from heterogeneous slip system/phase rate response. Micro-mechanism under low stress and low temperature (T < 0.3Tm) has been shown to be different from conventional rate sensitivity expectations. Hence the constitutive framework developed is dependent on the crystallographic orientation, properly capturing micro-scale anisotropic rate behaviour. The intrinsic rate anisotropy of the HCP α prism and basal and BCC β phase slip systems in Ti-6242, recently determined from micro-pillar and crystal plasticity modelling, have been utilised to investigate the structural strain rate sensitivities of colonies, polycrystals, bimodal and basket weave microstructures. The rate sensitivity of colony structures is dominated by the HCP α phase behaviour, at least for alloys containing up to ∼20% volume fraction β phase, and is largely independent of β-lath orientation. The apparent anisotropy of a1, a2 and a3 basal resolved shear stresses in Ti-6242 colonies is shown to originate from the local crystal stress states established as opposed to the α−β interfaces. Texture and α−β morphology are shown to affect rate dependence and to corroborate that the basal rate sensitivity is stronger than that for prism slip in Ti-6242. Morphological effects are shown to affect rate dependence but not strongly, but the number of HCP α phase variants in basketweave structures is found to have a significant effect with higher numbers of variants leading to lower strain rate sensitivities. This is potentially important in designing alloys to resist cold dwell fatigue

A mechanistic modelling methodology for microstructure-sensitive fatigue crack growth

A mechanistic methodology for simulating microstructurally-sensitive (tortuosity and propagation rate) fatigue crack growth in ductile metals is introduced which utilises the recently introduced dislocation configurational stored energy as the measure of the driving force. The model implements crystal plasticity finite element simulations using the eXtended Finite Element Method (XFEM) to represent the crack. Two methods of predicting the direction of growth (based on the crystallographic slip or the maximum principal stress) are compared. The crystallographic slip based direction model is shown to predict microstructurally-sensitive fatigue crack growth in single crystals which displays many features of path tortuosity that have been observed experimentally. By introducing a grain boundary, the crystallographic model is shown to capture behaviour similar to that observed experimentally including crack deflection and retardation at the grain boundaries. Finally, two experimental examples of fatigue cracks growing across three grains are analysed, and the model is shown to capture the correct crystallographic growth paths in both cases

On cold dwell facet fatigue in titanium alloy aero-engine components

This paper investigates the mechanisms of facet nucleation through combining aero-engine manufacturer disc component test data with microstructure-sensitive crystal plasticity finite element (CPFE) models. Full-scale component testing has been carried out in a manner representative of in-service conditions. Elastic FE analyses of discs under these conditions and fully accounting for thermal and residual processing strains have also been carried out. Disc facet nucleation sites have been identified and the local stress states evaluated in order to establish crystal plasticity oligocrystal sub-models. The oligocrystal RVE models provide knowledge of hard-soft grain stresses under dwell loading, and the consequent load shedding in order to provide stresses required for the facet nucleation. The disc component facet observations together with the crystal plasticity sub-model oligocrystal approach provide persuasive evidence that a hard-soft grain combination is required for facet formation, that the remote stress state influences the resolved shear stress on the soft grain initiating slip (with tensile uniaxial stress state more damaging than a tension-tension biaxial stress state), and that the load shedding which results is essential in pushing up the hard-grain basal stress to nucleate facets

Competing mechanisms of particle fracture, decohesion and slip-driven fatigue crack nucleation in a PM nickel superalloy

Fatigue cracks may initiate around non-metallic inclusions via particle fracture, particle decohesion and slip-driven nucleation. Cohesive zone techniques within microstructurally faithful crystal plasticity modelling validated by micromechanical experiments (HR-DIC and HR-EBSD) are employed to investigate these nucleation phenomena. Particle fracture and decohesion lead to stress redistribution which influences subsequent energy storage driving slip-driven fatigue crack nucleation. Particle fracture and decohesion strengths were determined and using a stored energy criterion, the number of cycles to initiation of the fatigue microcrack was predicted. A threshold applied stress below which decohesion and fracture do not occur was obtained, thus modestly increasing fatigue life

A robust and efficient hybrid solver for crystal plasticity

Conventional crystal plasticity (CP) solvers are based on a Newton-Raphson (NR) approach which use an initial guess for the free variables (often stress) to be solved. These solvers are limited by a finite interval of convergence and often fail when the free variable falls outside this interval. Solution failure results in the reduction of the time increment to be solved, thus convergence of the CP solver is a bottleneck which determines the computational cost of the simulation. The numerical stability of the slip law in its inverted form offers a solver that isn't vulnerable to poor pre-conditioning (initial guess) and can be used to progress to a solution from a stable starting point (i.e., from zero slip rate γ˙pk=0 s−1). In this paper, a novel formulation that enables the application of the slip law in its inverted form is introduced; this treats all slip systems as independent by approximating the Jacobian as a diagonal matrix, thus overcomes ill-defined and singular Jacobians associated with previous approaches. This scheme was demonstrated to offer superior robustness and convergence rate for a case with a single slip system, however the convergence rate for extreme cases with several active slip systems was relatively poor. Here, we introduce a novel ‘hybrid scheme’ that first uses the reverse scheme for the first stage of the solution, and then transitions to the forward scheme to complete the solution at a higher convergence rate. Several examples are given for pointwise calculations, followed by CPFEM simulations for FCC copper and HCP Zircaloy-4, which demonstrated solver performance in practise. The performance of simulations using the hybrid scheme was shown to require six to nine times fewer increments compared to the conventional forward scheme solver based on a free variable of stress and initial guess based on a fully elastic increment

A crystal plasticity investigation of slip system interaction, GND density and stored energy in non-proportional fatigue in Nickel-based superalloy

A dislocation and gradient-based crystal plasticity finite element study of fatigue has been carried out for nickel-based superalloy RR1000 in order to investigate detrimental non-proportional effects on fatigue life. Six differing multiaxial loading cycles including both proportional and non-proportional paths have been addressed and a critical stored energy density criterion employed for fatigue life. Non-proportional paths are shown to lead to higher numbers of intragranular slip system activations, reflecting experimental observations. These give higher geometrically necessary dislocation (GND) densities resulting from slip system interaction occurring through latent hardening effects in the model. The higher GND densities in turn drive up local stress and stored energy densities, thereby leading to lower predicted fatigue lives, in keeping with non-proportional fatigue experiments in the alloy considered. Intragranular slip system interaction may be the mechanistic explanation for non-proportional effects in fatigue of engineering alloys